Path regression models and process control optimisation

New regression methods to analyse multi-block and path models are presented. The multi-block and path data are assumed to be organised in a forward-oriented network of data blocks. This means that there are input data blocks, where modelling starts, and output data blocks that are at the end of the network. Input and output data blocks are connected by intermediate data blocks. It is shown how the method of partial least squares (PLS) regression can be extended to the data blocks that are connected in the path. A simple optimisation procedure in score space is presented, which determines optimal scores at normal operating conditions. It is shown how the optimisation procedure applies to any data block in the path. The advantage of the presented methods is due to that similar method as in PLS regression can be applied to any two connected data blocks. It is indicated that present methods are more efficient to carry out regressions than path methods presented in the literature. The results are illustrated by process data. Copyright (c) 2014 John Wiley & Sons, Ltd. It is assumed that data consist of data blocks, which are organised as a directed network. New regression methods between data blocks are presented. They start at the input blocks and show how input samples propagate through the path. A simple optimisation procedure is presented, which determines optimal score values for any score matrix in the path. Optimal scores and the methods of PLS regression are used to illustrate and improve the performance of the process.